83.26.12 problem 12

Internal problem ID [19336]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 01:34:31 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=4 x \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 26

dsolve(x^4*diff(y(x),x$4)+6*x^3*diff(y(x),x$3)+9*x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=4*x,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (c_3 \ln \left (x \right )+c_{1} \right ) \cos \left (\ln \left (x \right )\right )+\left (c_4 \ln \left (x \right )+c_{2} \right ) \sin \left (\ln \left (x \right )\right )+x \]

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 31

DSolve[x^4*D[y[x],{x,4}]+6*x^3*D[y[x],{x,3}]+9*x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+y[x]==4*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x+(c_2 \log (x)+c_1) \cos (\log (x))+(c_4 \log (x)+c_3) \sin (\log (x)) \]